Some species have different numbers of chromosomes, as we all know. Throughout evolution, how was a species able to survive with an extra chromosome? How was this organism able to breed successfully to form offspring with the additional chromosome?
Chromosome splits (or fusions for that matter) might not mean that much for reproductive success since genes can still line up and recombine. To quote the science blogger P.Z. Myers:
He illustrates it thusly:
So to answer your first question, changes in the number of chromosomes aren't always fatally deleterious (as you seem to think).
As for how a change in chromosome number might spread, the explanation is likely random drift and inbreeding. To quote P.Z. Myers again:
"Evolution" by Mark Ridley, p. 361 similarly points out that reproduction will be an uphill battle until the new variant becomes more common (often through inbreeding or drift in small populations):
This might in the end lead to speciation due to the two populations becoming incompatible.